Whole School Approach to Calculations Burton Bradstock Primary
Vocabulary
Underlying
mental facts
Adding
Year R/1
As outcomes, Year R/1 pupils should, for example:
Develop number bonds for all numbers up to 5 and of 10.
Reinforce in Y1. Develop counting on and back and then
complementary subtraction facts. No.s to 100, calculate
to 30
Year 1/2
As outcomes, Year 1/2 pupils should, for example:
Develop number bonds for 6 7 8 9 10 in Y1 and then up
to and including 20 in Y2. Develop counting on and back
and complementary subtraction facts. Calculate to 100s
Developing maths through practical and real life
opportunities including topic, story, welly walks, PE,
cooking, games and music. Sorting and modelling number
sentences. Approximate first.
Developing and building on mental strategies, explaining
orally e.g. combining 2 sets and showing stories as
number sentences, looking for pairs of numbers that make
10. Introduce +/-/= symbols. Approximate first. Explore
commutativity.
Moving to :l
l
l partially numbered lines
0
50
100
+
+
=
Sum
+
0
How many altogether?
Total
+
Increase
Can you find one more?
Moving to blank numberlines.
Continue supporting mental methods using blank
numberlines:-205 + 176 = 381
+100
+
0
1
2
3
4
5
6
7
+ 10
8
Plus
+
Altogether
+1 +1
25
Use Numicon imagery to support number
understanding.
35
+1
36 37
205
38
Bridging through a multiple of 10 by partitioning:57 + 6 into 57+3 + 3
+3
+3
+
57
60
63
Counting on
Partitioning into tens and units 25 + 13 becomes
20 + 10 with 5 + 3 which is 30 + 8 = 38
Use Numicon imagery to support understanding.
+70
305
+5
375
+1
380 381
Develop expanded method of addition (least
significant digit first) as a written method.
200 + 30 + 7
+ 100 + 40 + 5
300 70 12 = 382 Count on to establish total
Contract to standard algorithm when pupils ready:237
+ 145
Ensure pupils understand place value
382
involved in carrying
Use Deines imagery to support understanding.
1
Subtract

See notes above. Count back to take away and count on
to find out how many more than.
See notes above. Count back on numberlines to take
away and count up to find the difference.
See notes above. Maintain counting back to take
away.
Start with selves and objects moving gradually to bead
strings then numbered lines to find 1 less than:-
Starting with objects moving gradually to bead strings to
find 1 then 10 less than
Count on to find the difference using empty
numberlines, bridging through 10 initially:345 – 337 = 337 + 3 + 5 The difference is 8
Find the
difference

Minus

Take away
0 1 2 3 4 5 6
7
Taking away in real life:6 children playing Tug of War. Three fall over! How many
are left standing?
When ready move to counting back on a numberline by
partitioning only the necessary numbers:- 84 – 13 =
-1
-1
-1
-10
71
72
73
74
84
+100
+30
-1
7 423
7 523
7 552 7 553
Visualise when ready.
Expanded horizontal adding least significant
digits first. 4+ digits whole no. moving to
decimals and 3dp
+
7000 500 80 7
600 70 5
8000 200 60 2
1000 100 10
Contract to standard written method as pupils
ready:
7376
+ 439
7,815
11
Extend method to mixed
decimals, converting decimals to fractions:2.4 + 3.6 becomes: 24 tenths + 36
tenths=60 tenths (6 units).
See notes above. Maintain use of empty
numberlines to support mental calculation for
counting on and back
Use numberlines to cross thousands
boundaries:2003 - 7
+5
-3
-4
337
340
345
Explore, choosing the most efficient strategy for the
numbers involved.
Start to develop an expanded written method without
decomposition:- 167-54
Develop fact families for inverses:3 + 17 = 20 so
17 + 3 = 20 and
20 – 3 = 17 and also
20 – 17 = 3
Explore why subtraction is not commutative.
100+ 60+ 7
50+ 4
100 10 3 = 113 Count on to establish total and
contract when ready. Include decomposition.
Support with arrow cards and deines apparatus. Incl
decomposition when ready
1996
2000
Sandy blows 8 bubbles
are left?
2 pop! How many
September 2016
2003
Revisit written methods including
decomposition, first expanded then compacted
as pupils become ready:2793 – 148
Counting back
Less than
+3
Comparing to find the difference:
Year 5/6
As outcomes, Year 5/6 pupils should e.g.:
Develop no. bonds to 1000 and decimals to
10. In Y6 develop decimal number bonds to 1.
Count on and back and develop
complementary subtraction facts. Y5
1,000,000 Y6 10million
Maintain mental strategies, checking
procedures. Approximate first. Use many
worded problems.
Calculating to TTh, HTh, millions
Maintain empty box sentences and
numberlines with partitioning, negative
numbers and decimals. Use to calculate time
duration
7 423 + 129
Maintain use of inverses through empty box
sentences:- 37 +
= 82
Finding the largest number to put first :-  
Adding from the largest number first partitioning the
second number:- 25 + 13 (25 + 10 + 1 + 1 + 1)
Moving to numbered lines when ready
Year 3/4
As outcomes, Year 3/4 pupils should e.g.:
Develop no. bonds for 100, multiples of 5 to 100, then
multiples of 10 to 1000. Count on and back and
develop complementary subtraction facts. Explore
no.s to 1000s, Y3 calculate 3 digits and Y4 calculate
4 digits. Include negative and fractional numbers.
Continue building on existing mental strategies,
explaining orally and some use of negative numbers
in context. Approximate first. Establish checking
procedures. Use worded problems.
Y3 = 3 dig Y4= 4 dig
Partition into T and U to support mental methods:37+45
30+40 = 70
7+ 5 = 12
70 + 12 = 82
13
81
2000 700 90 3
100 40 8
2000 600 40 5
80
2793
- 148
2645
Extend to subtraction of decimals.
Whole School Approach to Calculations Burton Bradstock Primary
Vocabulary
Underlying
mental facts
Multiplication
Arrays
X
Year R/1
Year 1/2
Year 3/4
Year 5/6
As outcomes, Year R/1 pupils should, for example:
As outcomes, Year 1/2 pupils should, for example:
As outcomes, Year 3/4 pupils should e.g.:
As outcomes, Year 5/6 pupils should e.g.:
Develop tables facts for 2 then in Y1for 5 and 10 using
shapes to help visual learners. Secure so chn have
rapid recall of these facts and use to find and learn
division facts. Count back and forth in repeated steps of 2
in Yr moving to steps of 5 and 10 in Y1.
Develop tables facts for 5 and 10 in Y1 then in Y2 for 3
and 4 using shapes to help visual learners. Secure so
chn have rapid recall of these facts and use to find and
learn division facts. Count back and forth in repeated
steps of 5 and 10 in Y1 moving to 3 and 4 in Y2.
Develop tables facts for 6, 8, 9 and 7, 11 and 12
times table. Secure so chn have rapid recall of these
facts and use to find and learn division facts. Count
on and back in repeated steps of 6, 8, 9, 12, 7 and
11. Develop x/÷ by 10 and then by 100, 0+1
Develop concept of equal groups through looking at equal
groups in the real world moving to partitioning sets of
objects into equal 'lots of'.
Building on existing ideas, explain orally and keep focus
on equal 'lots of'. Use word problems.
Build on existing ideas, maintaining explanations and
word problems Consolidating EQUALITY of groups.
Secure rapid recall of all multiplication and
division facts up to 12x12 and develop table
facts up to 20x alongside squared, cubed,
prime and triangular no.s. Count on and back
in repeated steps of any size including decimal
steps and fraction steps. Develop x/÷ by 1000
and then by 0.1
Build on existing ideas, maintaining and
developing the grid method and arrays.
Practically double numbers up to 20 and record in number
sentences:-
Count on to link repeated addition to multiplication
based on times table facts:- 9 x 3 =, 27 etc
+ 3 +3 +3 +3 +3 +3
+3
+3 +3
HTU x TU, HTU x HTU, ThHTU x U and
decimals
246.7 x 7
Equal groups:- socks come in equal group of 2s, every
glove has an equal group of 5 fingers, so if I have 2
2 equal groups of 3 are 6.
3 x 2 = 6 linking ‘2 lots of 3’ to
repeated addition 3+ 3 = 6.
Double
X
Product
gloves, I have 2 equal groups of 5.
5
fingers and 5 more fingers. 5+5 beginning to understand
double as being the same as adding 5 twice.
X
Times
X
Equal lots
of/sets
of/groups of
X
Multiples
X
Repeated
addition
Use arrays to support
understanding.
Further develop idea of repeated addition as multiplying:5 added 3 times is 5 + 5 + 5 or 3 equal lots of 5 or
3 times 5 or 5 x 3
Support with practical work and rectangular arrays:Explore the concept that
multiplication can be done
in any order and model on
a numberline.
If there are 8 of us and we all have 2
legs. How many legs are there altogether?
Teddies have 2 badges on
their jumpers. How many
teddies’ jumpers could we
make with 10 badges?
See above. Link division to multiplication.
Division
÷
Introduce x symbol.
Practical division as sharing:- When we share 6 sweets
equally between 3 plates, there are 2 sweets on each.
0
2
4
6
100
35
5
 100 + 35 = 135
6
Develop the grid method TU x TU and HTU x U
32 x 14 x
30
2
10
8
Use Numicon for repeated addition and subtraction.
See above. Maintain practical division reinforcing equal
groups in both sharing and grouping eg how many cars
can be constructed using equal groups of 4 wheels per car
if I have 23 wheels? 5 cars with 3 left over wheels.
-4
-4
-4
Halve
1 lot
1 lot
1 lot
1 lot
1 lot
÷
Of 4
of 4
of 4
of 4
Factors
÷
Equal lots
of/groups
0
Practical dividing into equal groups of :We have 10 socks and we know they come in equal
groups of 2. How many pairs can we make?
7
-4
11
15
Use Arrays to support
understanding.
23
Link to repeated subtraction:- 6 crackers shared equally
between
2 plates = 3 each
I take away
1 from the 6 crackers for
the first plate, then I take away 1 from the remaining 5
crackers for the second plate…
'There are 18 apples in a box. How many bags of 6
320
+ 128
8
4 120
448 count on orally –
320, 420, 440, 448
Move to long multiplication duringY4 when ready
Maintain practical sharing. Focus on division as
grouping, including remainders.
Use multiples of the divisor (chunking) horizontally
TU  U
37  2 = 18 lots of 2 with 1 left over
-6
-10
-20
300
3 lots
of 2
Of 4
19
apples can be filled?'
÷
Repeated
subtraction
3
-4
0
3
6
9
12
15
18 21 24 27
Continue to develop rectangular arrays consolidating
understanding that multiplication can be done in any
order and is all about EQUAL groups:






Introduce grid method TU x U counting on orally
x
20
7
September 2016
5 lots of 2
10 lots of 2
If I know 1 lot of 3 is 3 then I can work out
(double) 2 lots of 3 is 6
(double) 4 lots of 3 is 12
173 ÷ 3 = 57 r2
(x 10) 10 lots of 3 is 30
(halve) 5 lots of 3 is 15 and then I know that 50x3=150
2 lots of 3
7
200
1400
40
280
6
42
0.7
0.49
= 1722.49
Maintain mental strategies:factorising
567x20 = (567x2) x 10
distributive 274 x11 = (274x10)+(274x1)
Develop short multiplication standard written
method:126
4.8 then long multiplication 567
x3
x 3
x 24
378
14.4
2268
1
2
11340
13608
20
1
7
17
37
Develop HTU ÷ U and Top Tips 173 ÷ 3 What do we
already know about equal groups of 3?...
-6
=3
Develop fact family explicit linking of multiplication and
division e.g.
2 x 3 = 6 so
6 ÷ 3 = 2 and also
3 x 2 = 6 and
6÷2=3
Moving to larger no.s as ready.
X
-12
4 lots of 3
-3
-150
1 lot
50 lots of 3
0 2
8
20 23
173
Maintain fact family work and use of inverses.
Use and apply in word problems rounding up and
down for context (Level 3). Including calculator use.
Move to vertical presentation during Y4.
Develop rules of divisibility for 2, 4, 8, 5, 10, 3,
6, 9 and reinforce link with multiplication to
support mental strategies. Chunk using
multiples of the divisor vertically HTU  TU
using Top Tips + chunking of 4-dig x 2 - dig
977  36
Top Tips – 1 36
2 72 so 20 lots = 720
4 144
10 360 (and use to derive
5 180
new info)
977
moving to:- 360 10 lots
617
- 360 10 lots
257
- 180 5 lots
77
- 72 2 lots
5
Answer: 27 5/36 or
Short division in Y5, 12 1
Introduce BODMAS
4 484
977
360 10x36
617
360 10x36
257
180 5x36
77
72 2x36
5
27 r5